A8952. k-Multiple Free Set

A $k$ -multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by $k$ . That is, there are no two integers $x$ and $y$ $(x<y)$ from the set, such that $y=x·k$ .

You're given a set of $n$ distinct positive integers. Your task is to find the size of it's largest $k$ -multiple free subset.

The first line of the input contains two integers $n$ and $k$ ( $1<=n<=10^{5},1<=k<=10^{9}$ ). The next line contains a list of $n$ distinct positive integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{9})$ .

All the numbers in the lines are separated by single spaces.

On the only line of the output print the size of the largest $k$ -multiple free subset of ${a_{1},a_{2},...,a_{n}}$ .

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.